-7/3y-5/4=5/4y+3

Solution for -7/3y-5/4=5/4y+3 equation:

-7/3y-5/4=5/4y+3

We move all terms to the left:

-7/3y-5/4-(5/4y+3)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 4y+3)!=0

y∈R


We get rid of parentheses

-7/3y-5/4y-3-5/4=0

We calculate fractions


(-448y)/192y^2+(-15y)/192y^2+(-15y)/192y^2-3=0

We multiply all the terms by the denominator


(-448y)+(-15y)+(-15y)-3*192y^2=0

Wy multiply elements

-576y^2+(-448y)+(-15y)+(-15y)=0

We get rid of parentheses

-576y^2-448y-15y-15y=0

We add all the numbers together, and all the variables

-576y^2-478y=0

a = -576; b = -478; c = 0;
Δ = b2-4ac
Δ = -4782-4·(-576)·0
Δ = 228484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{228484}=478$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-478)-478}{2*-576}=\frac{0}{-1152}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-478)+478}{2*-576}=\frac{956}{-1152}
=-239/288
$